Does prophecy make the hero less heroic?

In movies like Tim Burton's Alice in Wonderland and in the Harry Potter movies, there were prophecies that stated the main protagonists (Alice, Harry) would be the ones to defeat the main villains. I'm fairly certain that the comics have similar situations. This seems to bug he for some reason. It just seems like the hero of the story is just doing what fate wants and not actually being the hero that they are. They do still save the day and all, but it just feels like they had no control over actually being or becoming the hero.

So my question is: Are heroes less heroic when they are only doing what fate has decided?

It only makes them heroic when fulfilling their destiny means sacrifice (which is the case, half the time).

I was never a fan of hero-via-prophecy. Not that I haven't read, watched, etc stories where that happens and enjoyed them. I do agree that something is lost. Without the element of the hero's free will and choice to take up the task it's ultimately less impactful. They're less a hero and more a victim of circumstance.

@aros001: I think it was a 2-way street in Harry Potter, either Harry or Voldemort were both prophesied to be only able to be killed by each other.

The prophecy is usually very vague, it can be interpreted the multiple ways. So it doesn't make the character less heroic. It casn even add to the strain the hero already feels (the prophecy about Buffy killed by Master Vampire, for example).

Exactly. I just feel it's more heroic when the hero is doing what they are doing because it's the right thing to do, not just because it was foretold that they would. This is what bugs me about "chosen ones". The only reason everyone believed that they were so great and gave them a chance was because a prophecy said they would do something (Anakin Skywalker, for example).